2022 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 12 Easy

A pair of fair 6-sided dice is rolled n times. What is the least value of n such that the probability that the sum of the numbers face up on a roll equals 7 at least once is greater than \dfrac{1}{2}?

  • A.

    2

  • B.

    3

  • C.

    4

  • D.

    5

  • E.

    6

Answer:C

For each roll, the probability to have a sum of 7 is \frac 16.

To make the probability that the sum of the numbers face up on a roll equals 7 at least once is greater than \frac 12, we have P(\text{sum not 7})=1-\left(\frac 56 \right)^n<\frac 12, where n_{min}=4.

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